Car runs for 3 minutes or one kilometer then the temp gauge goes to red line
hot. Turns off engine and wait for 4-5 minutes to cool and it goes back to
median. Runs again for 3 minutes or about half a mile or one kilometer and
the gauge goes up again to hot.Was able to limp home using this cycle.

Upper radiator hose is very hot, lower hose is is just lukewarm. Got home
and allowed t he engine to cool a bit. Removed the cap. Revving the engine
and peeking through the open radiator cap doesn't produce any water flow but
the level rises a bit. I don't think its the head gasket for I don't see any
small bubbles coming out.

Could it be that the thermostat is stuck closed? Pump defective?